Abstract
In this note we show that the renewal function $H$ corresponding to a random walk with positive mean $\mu$ and finite variance $\sigma^2$ satisfies the inequality $H(x) < \mu^{-1} x + 3(1 + \mu^{-2}\sigma^2)$.
Citation
Charles J. Stone. "An Upper Bound for the Renewal Function." Ann. Math. Statist. 43 (6) 2050 - 2052, December, 1972. https://doi.org/10.1214/aoms/1177690883
Information
Published: December, 1972
First available in Project Euclid: 27 April 2007
zbMATH: 0257.60030
MathSciNet: MR356270
Digital Object Identifier: 10.1214/aoms/1177690883
Rights: Copyright © 1972 Institute of Mathematical Statistics
